From Philosophical Program to Formal Science: The Complete Axiomatization, Dual Realization and Machine Verification of YuanXian Theory (YXT)

This paper presents the complete transition of YuanXian Theory (YXT) from a philosophical-physical program aimed at unifying physics, mathematics, consciousness and life, into a fully formalized, computable, and machine-verifiable scientific theory. Grounded in four core axioms — True-Circle Self-Consistency (TCSC), Spacetime Manifold Uniqueness (STM), Factor Conservation (FSC), and Self-Referential Mind-field Generation (SRM) — the theory is rigorously realized in two foundational systems: Self-Referential Mind-Field Type Theory (YXTT) based on Homotopy Type Theory, and an ontological extension of ZFC set theory.We prove the equivalence of both realizations and derive numerous testable consequences, including the theoretical computation of 24 fundamental physical constants with high precision, a conditional proof of the Riemann Hypothesis, the rigorous theorem that the total energy of the universe is zero, and the prediction of the True-Circle Self-Referon (TCSR) particle. All formalizations and proofs have been machine-verified in Lean 4 and Coq and are fully open-sourced.本文系統闡述了元憲理論(YuanXian Theory, YXT)從旨在統一物理、數學、意識與生命的哲學-物理學綱領,發展為具備嚴格數學實現、可計算且可機器驗證的形式科學理論的完整過程。該理論以四大核心公理——真圓自洽性(TCSC)、時空流形唯一性(STM)、宇宙因素守恒(FSC)與自指心場生成(SRM)——為基礎,在自指心場類型論(YXTT,基於同倫類型論)與 ZFC 集合論擴展中實現雙重形式化,並證明二者同構等價。基於此,我們導出 24 個基本物理常數的高精度理論值、黎曼猜想的條件性證明、宇宙總能量嚴格為零定理,以及真圓自指子(TCSR)粒子預言。全部形式化內容已在 Lean 4 與 Coq 中完成機器驗證,並完全開源。